Article Sidebar

Download
Statistic
Read Counter : 35

Downloads

Download data is not yet available.

Main Article Content

Abstract

Many studies have reported that functional thinking plays a crucial role in mathematical problem-solving, particularly in fields requiring analytical reasoning, such as maritime studies. However, existing research has yet to comprehensively explore the specific task characteristics that effectively stimulate functional thinking in mathematical problem-solving, particularly among maritime students who must apply these skills in solving safety-of-life problems at sea. Addressing this gap, the present study investigates the potential of mathematical tasks in fostering functional thinking among second-semester students enrolled in the Deck Officer Program in Indonesia. The study involved three students with different mathematical abilities, who were given problem-solving tasks. Their responses were observed, recorded, and analyzed based on their written work. The findings reveal that non-routine problems involving functional situations—where students generalize relationships between varying quantities to determine function rules—effectively promote functional thinking. This is evidenced by the emergence of key functional thinking components, including problem identification, data representation, pattern recognition, covariational and correspondence relationships, and the evaluation of generalization rules. These results contribute to the development of research instruments in mathematics education and provide valuable insights for researchers and educators seeking to enhance functional thinking through task design.

Keywords

Functional Thinking Mathematical Problem-Solving Research Instruments Task

Article Details

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite
Tarida, L., Budiarto, M. T., & Lukito, A. (2025). The potential problem to explore students’ functional thinking in mathematical problem-solving. Journal on Mathematics Education, 16(1), 275–298. https://doi.org/10.22342/jme.v16i1.pp275-298
Download Citation
Endnote/Zotero/Mendeley (RIS)
BibTeX

References

  1. Aguilar, J., & Telese, J. A. (2018). Mathematics understanding of elementary pre-service teachers: The analysis of their procedural-fluency, conceptual-understanding, and problem-solving strategies. Mathematics Teaching-Research Journal, 10(3–4), 24–37.
  2. As’ari, A. R., Kurniati, D., Maharani, S., & Basri, H. (2019). Ragam soal matematis untuk mengembangkan disposisi berpikir kritis. (Issue 112). Universitas Negeri Malang.
  3. Blanton, M. L., & Kaput, J. J. (2011). Functional Thinking as a Route Into Algebra in the Elementary Grades. Early Algebraization, 5–23. https://doi.org/10.1007/978-3-642-17735-4_2
  4. Blanton, M., Stephens, A., Knuth, E., Gardiner, A. M., Isler, I., & Kim, J.-S. (2015). The development of children’s algebrai thinking: The impact of a comprehensive early algebra intervention in third grade. Journal for Research in Mathematics Education, 46(1), 39–87. https://doi.org/10.5951/jresematheduc.46.1.0039
  5. Chapra, S. C., & Canale, R. P. (2011). Numerical Methods for Engineers (Vol. 1221). New York: Mcgraw-hill.
  6. Chimoni, M., Pitta-Pantazi, D., & Christou, C. (2023). Τwo Different Types of Technologically Enhanced Intervention Modules To Support Early Algebraic Thinking. Education and Information Technologies, 28(3), 3417–3441. https://doi.org/10.1007/s10639-022-11331-x
  7. Confrey, J., & Smith, E. (1991). A framework for functions: Prototypes, multiple representations, and transformations. Proceedings of the Thirteenth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, 1, 57–63. http://eric.ed.gov/?id=ED352274
  8. Creswell, J. W., & Poth, C. N. (2016). Qualitative inquiry and research design: Choosing among five approaches. Sage publications.
  9. Denzin, N. K., & Lincoln, Y. S. (2011). The Sage handbook of qualitative research. Sage.
  10. Ding, R., Huang, R., & Deng, X. (2023). Multiple pathways for developing functional thinking in elementary mathematics textbooks: a case study in China. Educational Studies in Mathematics, 114(2), 223–248. https://doi.org/10.1007/s10649-023-10237-w
  11. Fatmanissa, N., Yuli Eko Siswono, T., Lukito, A., & Ismail, I. (2024). Utilizing Decision-making Task: Students’ Mathematical Justification in Collaborative Problem Solving. Avances de Investigación En Educación Matemática, in press, 1–21. https://doi.org/https://doi.org/10.35763/aiem26.5341
  12. Frey, K., Sproesser, U., & Veldhuis, M. (2022). What is functional thinking ? Theoretical considerations and first results of an international interview study. Twelfth Congress of the European Society for Research in Mathematics Education (CERME12).
  13. Günster, S. M., & Weigand, H. G. (2020). Designing digital technology tasks for the development of functional thinking. ZDM - Mathematics Education, 52(7), 1259–1274. https://doi.org/10.1007/s11858-020-01179-1
  14. Huang, L. (2023). A Mathematical Modeling and an Optimization Algorithm for Marine Ship Route Planning. Journal of Mathematics, 2023. https://doi.org/10.1155/2023/5671089
  15. Jamaliyatul, N. A. A. H., Badyalina, B., Mokhtar, N. A., Rambli, A., Zubairi, Y. Z., & Ghapor, A. A. (2023). Modelling Wind Speed Data in Pulau Langkawi With Functional Relationship. Sains Malaysiana, 52(8), 2419–2430. https://doi.org/10.17576/jsm-2023-5208-18
  16. Jamil, A. F., Siswono, T. Y. E., Setianingsih, R., Lukito, A., & Ismail. (2023). The potential problem to explore metacognitive regulation in ollaborative problem-solving. Ricerche Di Pedagogia e Didattica, 18(1), 57–71. https://doi.org/10.6092/issn.1970-2221/16086
  17. Jamil, M. G., & Bhuiyan, Z. (2021). Deep learning elements in maritime simulation programmes: a pedagogical exploration of learner experiences. International Journal of Educational Technology in Higher Education, 18(1). https://doi.org/10.1186/s41239-021-00255-0
  18. Kaput, J. J. (2008). What is algebra? What is algebraic reasoning? In Algebra In The Early Grades (pp. 5–18). Routledge.
  19. Khusna, A. H., Yuli, T., Siswono, E., & Wijayanti, P. (2024). Mathematical Problem Design to Explore Students ’ Critical Thinking Skills in Collaborative Problem Solving. Mathematics Teaching-Research Journal, 16(3), 217–240.
  20. KNKT. (2018). Laporan Investigasi Kecelakaan Kapal Laut Tenggelamnya KM. Sinar Bangun 4 Tahun 2018. Kementerian Perhubungan, 1–53. http://knkt.dephub.go.id/knkt/ntsc_maritime/Laut/2018/FINAL KNKT-18-06-18-03 Sinar Bangun 4-Final PrintA.pdf
  21. Kriegler, S. (2004). Just What is Algebraic Thinking? Mathematics Educator, 8(1), 139–151.
  22. Lichti, M., & Roth, J. (2018). How to Foster Functional Thinking in Learning Environments Using Computer-Based Simulations or Real Materials. Journal for STEM Education Research, 1(1–2), 148–172. https://doi.org/10.1007/s41979-018-0007-1
  23. Lincoln, Y. S., & Guba, E. . (1985). Naturalistic Inquiry. In The A-Z of Social Research. SAGE Publications Inc. https://doi.org/10.4135/9781412986281.n232
  24. Martins, R., Viseu, F., & Rocha, H. (2023). Functional Thinking: A Study with 10th-Grade Students. Education Sciences, 13(4). https://doi.org/10.3390/educsci13040335
  25. Mycroft, K., & Sriraman, B. (2021). Mathematics in the Maritime. In Handbook of the Mathematics of the Arts and Sciences. https://doi.org/10.1007/978-3-319-57072-3_137
  26. Noor, N. M., Mustafa, M., Bakri, A., Yahaya, A. S., & Ramli, N. A. (2015). Replace The Missing Values In Environmental Data Set. 803, 278–281. https://doi.org/10.4028/www.scientific.net/MSF.803.278
  27. OECD. (2023). Program For International Student (PISA) 2022 Assessment and Analytical Framework. In OECD (Organisation for Economic Co-operation and Development) Publishing. https://www.oecd-ilibrary.org/education/pisa-2022-assessment-and-analytical-framework_dfe0bf9c-en
  28. Oliveira, H., Polo-Blanco, I., & Henriques, A. (2021). Exploring prospective elementary mathematics teachers’ knowledge: A focus on functional thinking. Journal on Mathematics Education, 12(2), 257–278. https://doi.org/10.22342/jme.12.2.13745.257-278
  29. Oneto, L., Coraddu, A., Cipollini, F., Karpenko, O., Xepapa, K., Sanetti, P., & Anguita, D. (2018). Crash Stop Maneuvering Performance Prediction: a Data-Driven Solution for Safety and Collision Avoidance. Data-Enabled Discovery and Applications, 2(1). https://doi.org/10.1007/s41688-018-0024-3
  30. Pang, J., Leena, L., & Sunwoo, J. (2022). Task Development to Measure Functional Thinking: Focusing on Third Graders’ Understanding. The Korean Society of Educational Studies in Mathematics - Journal of Educational Research in Mathematics, 32(3), 351–372. https://doi.org/10.29275/jerm.2022.32.3.351
  31. Pang, J. S., & Sunwoo, J. (2022). Design of a pattern and correspondence unit to foster functional thinking in an elementary mathematics textbook. ZDM - Mathematics Education, 54(6), 1315–1331. https://doi.org/10.1007/s11858-022-01411-0
  32. Pitta-Pantazi, D. (2020). Different Types of Algebraic Thinking: an Empirical Study Focusing on Middle School Students. International Journal of Science and Mathematics Education, 18(5), 965–984. https://doi.org/10.1007/s10763-019-10003-6
  33. Pitta-Pantazi, D., Chimoni, M., & Christou, C. (2020). Different Types of Algebraic Thinking: an Empirical Study Focusing on Middle School Students. International Journal of Science and Mathematics Education, 18(5), 965–984. https://doi.org/10.1007/s10763-019-10003-6
  34. Pittalis, M. (2023). Young Students’ Arithmetic-Algebraic Structure Sense: an Empirical Model and Profiles of Students. International Journal of Science and Mathematics Education, 21(6), 1865–1887. https://doi.org/10.1007/s10763-022-10333-y
  35. Pittalis, M., Sproesser, U., Demosthenous, E., & Odysseos, E. (2024). Enhancing functional thinking in grade 5–6 students through a dynamic mathematics intervention program. In Education and Information Technologies (Issue 0123456789). Springer US. https://doi.org/10.1007/s10639-024-12865-y
  36. Rolfes, T., Roth, J., & Schnotz, W. (2021). Mono- and Multi-Representational Learning of the Covariational Aspect of Functional Thinking. Journal for STEM Education Research, 5(1), 1–27. https://doi.org/10.1007/s41979-021-00060-4
  37. Rott, B., Specht, B., & Knipping, C. (2021). A descriptive phase model of problem-solving processes. ZDM - Mathematics Education, 53(4), 737–752. https://doi.org/10.1007/s11858-021-01244-3
  38. Sanjaya, A., Johar, R., Ikhsan, M., & Khairi, L. (2018). Students’ thinking process in solving mathematical problems based on the levels of mathematical ability. Journal of Physics: Conference Series, 1088. https://doi.org/10.1088/1742-6596/1088/1/012116
  39. Schoenfeld, A. H. (1985). Mathematical problem solving. In Academic Press. Academic Press. https://doi.org/10.1007/BF00305624
  40. Schoenfeld, A. H. (2006). Problem Solving from Cradle to Grave. Annales de Didactique et de Sciences Cognitives, 11, 41–73.
  41. Schoenfeld, A. H. (2016). Learning to Think Mathematically: Problem Solving, Metacognition, and Sense Making in Mathematics (Reprint). Journal of Education, 196(2), 1–38. https://doi.org/10.1177/002205741619600202
  42. Sibgatullin, I. ., Korzhuev, A. ., Khairullina, E. ., Sadykova, A. ., Baturina, R. ., & Chauzova, V. (2022). A Systematic Review on Algebraic Thinking in Education. Eurasia Journal of Mathematics, Science and Technology Education, 18(1), 1–15. https://doi.org/10.29333/EJMSTE/11486
  43. Smith, E. (2008). Representational Thinking as a Framework for Introducing Functions in the Elementary Curriculum. In J. Kaput, D. Carraher, & M. Blanton (Eds.), Algebra in the Early Grades. Mahwah, NJ: Lawrence Erlbaum Associates/Taylor & Francis Group and National Council of Teachers of Mathematics. https://doi.org/10.4324/9781315097435-6
  44. Stephens, A. C., Fonger, N., Strachota, S., Isler, I., Blanton, M., Knuth, E., & Murphy Gardiner, A. (2017). A Learning Progression for Elementary Students’ Functional Thinking. Mathematical Thinking and Learning, 19(3), 143–166. https://doi.org/10.1080/10986065.2017.1328636
  45. Sun, S., Sun, D., & Xu, T. (2023). The Developmental Progression of Early Algebraic Thinking of Elementary School Students. Journal of Intelligence, 11(12), 1–19. https://doi.org/10.3390/jintelligence11120222
  46. Taguma, M., Makowiecki, K., & Gabriel, F. (2023). OECD Learning Compass 2030: Implications for Mathematics Curricula. In New ICMI Study Series: Vol. Part F776. https://doi.org/10.1007/978-3-031-13548-4_33
  47. Tanişli, D. (2011). Functional thinking ways in relation to linear function tables of elementary school students. Journal of Mathematical Behavior, 30(3), 206–223. https://doi.org/10.1016/j.jmathb.2011.08.001
  48. Tarida, L., Budiarto, M. T., & Lukito, A. (2024). State of the Art of Functional Thinking, Scaffolding, Problem Solving and Self Efficacy (A Systematic Mapping Study). AIP Conference Proceedings, 3046(1). https://doi.org/10.1063/5.0194597
  49. Team, F., License, C. C., & By-sa, C. C. (2021). Vision document on Functional Thinking Pre-amble.
  50. Thompson, P. W., & Carlson, M. P. (2017). Variation, covariation, and functions: Foundational ways of mathematical thinking. Compendium for Research in Mathematics Education, November 2016, 421–456.
  51. Utami, N. S., Prabawanto, S., & Suryadi, D. (2023). How Students Generate Patterns in Learning Algebra? A Focus on Functional Thinking in Secondary School Students. European Journal of Educational Research, 12(2), 913–925. https://doi.org/10.12973/eu-jer.12.2.913
  52. Vollrath, H.-J. (1986). Search Strategies as Indicators of Functional Thinking. Educational Studies in Mathematics, 17, 387–400.
  53. Wahab, M. A. (2017). Interpolation and Extrapolation. Proc. Topics Syst. Eng. Winter Term, 17, 1–6. https://doi.org/10.1201/9781315120195-4
  54. Wakhata, R., Balimuttajjo, S., & Mutarutinya, V. (2023). Enhancing the Learning of Limits of Functions Using Multiple Representations. Mathematics Teaching-Research Journal, 15(2), 182–202.
  55. Warren, E., Miller, J., & Cooper, T. J. (2011). Exploring Young Students’ Functional Thinking. PNA, 7(2), 75–84.
  56. Wei, H., Bos, R., & Drijvers, P. (2023). An Embodied Approach to Abstract Functional Thinking Using Digital Technology: A Systematic Literature Review. International Journal of Technology in Mathematics Education, 30(2), 75–94. https://doi.org/10.1564/tme
  57. Wilkie, K. J. (2014). Upper primary school teachers’ mathematical knowledge for teaching functional thinking in algebra. Journal of Mathematics Teacher Education, 17(5), 397–428. https://doi.org/10.1007/s10857-013-9251-6
  58. Windsor, W. (2011). How Problem Solving Can Develop an Algebraic Perspective of Mathematics. Australian Primary Mathematics Classroom, 16(4), 8–13. http://eric.ed.gov/?id=EJ961653
  59. Wu, G., Zhao, M., Cong, Y., Hu, Z., & Li, G. (2021). Algorithm of berthing and maneuvering for catamaran unmanned surface vehicle based on ship maneuverability. Journal of Marine Science and Engineering, 9(3). https://doi.org/10.3390/jmse9030289
  60. Yuniati, S., Nusantara, T., Sulandra, I. M., & Suparjono. (2022). Investigating Functional Thinking Processes that Impact on Function Composition Problems in Indonesia. Acta Scientiae, 24(5), 84–118. https://doi.org/10.17648/acta.scientiae.6969
  61. Zhang, J. H., Meng, B., Zou, L. C., Zhu, Y., & Hwang, G. J. (2023). Progressive flowchart development scaffolding to improve university students’ computational thinking and programming self-efficacy. Interactive Learning Environments, 31(6), 3792–3809. https://doi.org/10.1080/10494820.2021.1943687